Can't access a subfolder due to the mod-rewrite

I’ve got a WordPress site installed here: https://www.r-bloggers.com

And I wish to install another WordPress site under the /lang directory:

https://www.r-bloggers.com/lang/

I created the subfolder and uploaded the files, but when I navigate to the folder, the site keeps telling me it’s a 404 page of the root directory website.

I imagine this has something to do with the mod-rewrite rules in the .htaccess of the root directory WP installation. I tried adding these line to the .htaccess:

[Code moderated as per the Forum Rules. Please use the pastebin]